What's the correct name of the Camera pyramid-shaped wireframe object used to display it?
The pyramid-shaped camera gizmo is just a shape commonly chosen to represent cameras. The pyramid's angle and direction depicts the camera's field of view. Unrelated to Blender, the term you are looking for is viewing frustum or pyramid of vision. This is intended for depicting the near and far clipping planes, but Blender does not show these in its camera gizmo. As such, the shape used in Blender is not technically even a frustum because the four segments converge to a point. Within the context of Blender, it is simply called the camera.